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Appendix VI.


and stud E. The latter is just so long as to keep the pointer D
touching but not indenting the paper. If an area be traced out
by the pointer D, the wheel H will roll on the paper, sometimes
forward and sometimes backward, but the net result will be
forward and will indicate on the vernier j, say in square inches,
the exact value of the area. If the net revolutions of H are more
than one, the observer must look at the dial L, where the turns
of H are registered by the worm wheel K, without the tedium of
personal counting. The theory of the instrument is very simple,
the wheel merely registering the difference of two total radial
areas N and M; but this knowledge is unimportant.

To use the instrument, let the tracer D be set to some point p
on the boundary of the area \ and note the readings on the
wheels L and H, and vernier j, as follow:

Reading on wheel L         = 2 +      =    20*00

     H      '   = 47+   =      470
Coincidence on vernier j = 2         =           2

Correct reading


Now trace the boundary by means of pointer r>, in the direction
of the arrow till point p is again reached, and take the reading
of the wheels again as, say, 29*65. The actual area will be
29-65 - 2472  4-93 sq. ins.

A special case occurs when the area is so large that it can
only be circumscribed by placing the pin point F within the
diagram. The procedure is not changed in the reading, tracing,
and re-reading; but the result must be increased by a certain
constant, which varies with different instruments and is marked
upon the weight c. For example, let

Reading after tracing

Add figure on weight




N.B. ^Differ-
ence' is positive or
negative, as found
by rough trial of
the area.

282*31 or 260*33 sq. ins.

The Planimeter is immensely useful for a variety of area